8-bit bitwise addition (full adder) implemented using only bitwise operations.

bitwise_add.c

/*
 * 8-bit bitwise addition (full adder) implemented using only bitwise operations.
 * Luke McCarthy 2021-10-06
 */

#include <assert.h>
#include <stdint.h>
#include <stdio.h>

static uint8_t carry(uint8_t A, uint8_t B, uint8_t C)
{
    return (A & B) | (B & C) | (C & A);
}

static uint8_t bitwise_add(uint8_t A, uint8_t B)
{
    uint8_t R, C;
    R = (A & 0x01) ^ (B & 0x01);
    C = carry(A & 0x01, B & 0x01, 0);
    R |= (A & 0x02) ^ (B & 0x02) ^ ((C & 0x01) << 1);
    C |= carry(A & 0x02, B & 0x02, (C & 0x01) << 1);
    R |= (A & 0x04) ^ (B & 0x04) ^ ((C & 0x02) << 1);
    C |= carry(A & 0x04, B & 0x04, (C & 0x02) << 1);
    R |= (A & 0x08) ^ (B & 0x08) ^ ((C & 0x04) << 1);
    C |= carry(A & 0x08, B & 0x08, (C & 0x04) << 1);
    R |= (A & 0x10) ^ (B & 0x10) ^ ((C & 0x08) << 1);
    C |= carry(A & 0x10, B & 0x10, (C & 0x08) << 1);
    R |= (A & 0x20) ^ (B & 0x20) ^ ((C & 0x10) << 1);
    C |= carry(A & 0x20, B & 0x20, (C & 0x10) << 1);
    R |= (A & 0x40) ^ (B & 0x40) ^ ((C & 0x20) << 1);
    C |= carry(A & 0x40, B & 0x40, (C & 0x20) << 1);
    R |= (A & 0x80) ^ (B & 0x80) ^ ((C & 0x40) << 1);
    C |= carry(A & 0x80, B & 0x80, (C & 0x40) << 1);
    return R;
}

int main()
{
    for (uint16_t A = 0; A < 256; A++) {
        for (uint16_t B = 0; B < 256; B++) {
            printf("%u + %u = %u\n", A, B, bitwise_add(A, B));
            assert(bitwise_add(A, B) == ((A + B) & 0xFF));
        }
    }
    return 0;
}